IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v178y2020icp328-344.html
   My bibliography  Save this article

A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method

Author

Listed:
  • Zhang, Zhe
  • Zhang, Jing
  • Ai, Zhaoyang
  • Cheng, FanYong
  • Liu, Feng

Abstract

In this paper, we propose a new General Stability Criterion (GSC) for the stability analysis of the nonlinear fractional-order systems(FOs) with time delay at all levels based on the deduction of Wirtinger inequality, Integral mean value theorem(IMVT), fractional-order Lyapunov method, and our initiated general Lemma (WILL Deduction Method). This proposed WILL-Deduction method initiates a general lemma to simplify the construction of the GSC. Therefore, the GSC prevails over the previous criteria in that it solves the stability puzzle of all FOs, including all kinds of time-delay with greater flexibility. For all the fractional-order parametersα∈0,1, the GSC is effective. In conclusion, the initially proposed GSC has generality and universality with more efficiency. Finally the numerical simulations have proved the correctness and universality of GSC .

Suggested Citation

  • Zhang, Zhe & Zhang, Jing & Ai, Zhaoyang & Cheng, FanYong & Liu, Feng, 2020. "A novel general stability criterion of time-delay fractional-order nonlinear systems based on WILL Deduction Method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 328-344.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:328-344
    DOI: 10.1016/j.matcom.2020.06.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420302214
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.06.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cruz-Victoria, Juan C. & Martínez-Guerra, Rafael & Pérez-Pinacho, Claudia A. & Gómez-Cortés, Gian Carlo, 2015. "Synchronization of nonlinear fractional order systems by means of PIrα reduced order observer," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 224-231.
    2. Momani, Shaher, 2005. "An explicit and numerical solutions of the fractional KdV equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(2), pages 110-118.
    3. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2009. "A note on the stability of fractional order systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1566-1576.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Silva-Juárez, Alejandro & Tlelo-Cuautle, Esteban & de la Fraga, Luis Gerardo & Li, Rui, 2021. "Optimization of the Kaplan-Yorke dimension in fractional-order chaotic oscillators by metaheuristics," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    3. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.
    4. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2018. "Applications of Lyapunov Functions to Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    5. Firoozjaee, M.A. & Yousefi, S.A., 2018. "A numerical approach for fractional partial differential equations by using Ritz approximation," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 711-721.
    6. Munoz-Pacheco, J.M. & Zambrano-Serrano, E. & Volos, Ch. & Tacha, O.I. & Stouboulos, I.N. & Pham, V.-T., 2018. "A fractional order chaotic system with a 3D grid of variable attractors," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 69-78.
    7. Chen, Yiming & Ke, Xiaohong & Wei, Yanqiao, 2015. "Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 475-488.
    8. Zhang, Xuefeng & Chen, Shunan & Zhang, Jin-Xi, 2022. "Adaptive sliding mode consensus control based on neural network for singular fractional order multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    9. Muñoz-Vázquez, Aldo Jonathan & Ortiz-Moctezuma, Manuel Benjamín & Sánchez-Orta, Anand & Parra-Vega, Vicente, 2019. "Adaptive robust control of fractional-order systems with matched and mismatched disturbances," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 85-96.
    10. Dongya Li & Xiaoping Zhang & Shuang Wang & Fengxiang You, 2022. "Robust Synchronization of Fractional-Order Chaotic System Subject to Disturbances," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
    11. Cai, Ruiyang & Ge, Fudong & Chen, YangQuan & Kou, Chunhai, 2019. "Regional observability for Hadamard-Caputo time fractional distributed parameter systems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 190-202.
    12. A.G., Soriano–Sánchez & C., Posadas–Castillo & M.A., Platas–Garza & A., Arellano–Delgado, 2018. "Synchronization and FPGA realization of complex networks with fractional–order Liu chaotic oscillators," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 250-262.
    13. Yang, Xue & Su, Yongmei & Yang, Liangli & Zhuo, Xinjian, 2022. "Global analysis and simulation of a fractional order HBV immune model," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    14. Huang, Chaobao & Yu, Xijun & Wang, Cheng & Li, Zhenzhen & An, Na, 2015. "A numerical method based on fully discrete direct discontinuous Galerkin method for the time fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 483-492.
    15. Orest Lozynskyy & Damian Mazur & Yaroslav Marushchak & Bogdan Kwiatkowski & Andriy Lozynskyy & Tadeusz Kwater & Bohdan Kopchak & Przemysław Hawro & Lidiia Kasha & Robert Pękala & Robert Ziemba & Bogus, 2021. "Formation of Characteristic Polynomials on the Basis of Fractional Powers j of Dynamic Systems and Stability Problems of Such Systems," Energies, MDPI, vol. 14(21), pages 1-35, November.
    16. Zhou, Xian-Feng & Yang, Fuli & Jiang, Wei, 2015. "Analytic study on linear neutral fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 295-307.
    17. Bahrampour, Elham & Asemani, Mohammad Hassan & Dehghani, Maryam, 2023. "Robust global synchronization of delayed incommensurate fractional-order gene regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    18. W. K. Zahra & S. M. Elkholy, 2012. "The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, August.
    19. Yan, Ye & Kou, Chunhai, 2012. "Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1572-1585.
    20. Zhang, Jia-Rui & Lu, Jun-Guo & Zhang, Qing-Hao, 2024. "Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case," Applied Mathematics and Computation, Elsevier, vol. 475(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:328-344. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.